Determination of the effective atomic number of materials using 59.54 keV gamma rays through theoretical approaches and MCNP simulation

In this Study, we aimed to calculate the effective atomic number ($Z_{\text{eff}}$) of commonly used alloy, polymer, and compound materials by computing Rayleigh and Compton scattering cross-sections using MCNP simulations and theoretical methods. The simulations were performed under experimental conditions, where the samples were exposed to emitted gamma rays from a ²⁴¹Am source, and the Rayleigh-to-Compton (R/C) ratio of them was measured at a 70° scattering angle with an HPGe detector. The simulation results shows that, $Z_{\text{eff}}$ values ranged from 6.32 (Bakelite) to 67.37 (HgI₂) across 25 materials. These values were also calculated using 15 theoretical methods and compared with available experimental results across different energies. Statistical analysis shows strong correlations (0.746–0.999) between material characteristics (ρ, μ_m, σ_a, σ_e, σ_m, N_e) and results from experimental, theoretical, and simulation methods. Correlation coefficients between simulation, experimental, and theoretical results, especially between experimental and simulation results are very high (0.997–0.999) with P-values below 0.008, which indicates the significance of the results of this Study and the effectiveness of this method in determining $Z_{\text{eff}}$ for different materials. Our results also showed that the dependence of the quantity R/C on $Z_{\text{eff}}$ for heavy and light materials are respectively $Z_{\text{eff}}^{4.38}$ and $Z_{\text{eff}}^{2.46}$.